Nominative: بَعْلَبَكُّ مَدِينَةٌ — ḍamma, no tanwīn.
Accusative: زُرْتُ بَعْلَبَكَّ — fatḥa, no tanwīn.
Genitive: سَافَرْتُ إِلَى بَعْلَبَكَّ — fatḥa, no tanwīn.
Remember: identify the word’s syntactic role first. Its case is not established merely by spotting a vowel.